Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models were used for modeling with heteroscedasticity data. This study aims to determine the time series model on the stock price data of PT Triputra Agro Persada Tbk. (TAPG) with modeling ARMA, ARCH and GARCH. Based on the smallest Akaike Information Criterion (AIC) and Schwarz Criterion (SC), it shows that the ARMA(1,0)-GARCH(2,1) model is the best model for predicting the value of TAPG stock prices.

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The optimal control problem is defined as a problem in determining the control u(t) that depends on time t, such that it produces the optimum value for the objective function. The optimal control system with constrained conditions can be changed to an optimal control system without constraints by constructing the value of u(t) so that u(t) is not constrained. In this research, we will examine how to determine an optimal control of a system of time-independent state space or Linear Time Invariant (LTI) with constrained states and minimize a given objective function. In addition, how to construct an optimal controller that is constrained to become an optimal controller without constraints using the penalty function method and its implementation using Matlab. The results of this study are that the optimal control is:.

Abstrak. Dalam artikel ini akan dikaji masalah realisasi positif stabil asimtotik darisuatu fungsi transfer yang memuat pole kompleks konjugat. Syarat perlu dan cukupuntuk eksistensi realisasi positif stabil asimtotik disajikan.Kata Kunci: Sistem linier diskrit, pole kompleks konjugat, realisasi positif stabil asimtotik